Professor Jerome Spanier
Edwin H. Spanier was born in Washington, D.C. in 1921 and educated at the Universities of Minnesota and Michigan. Spanier made his mark early in the mathematical community with his Ph.D. dissertation in the then rapidly expanding field of algebraic topology. Spanier's research in algebraic topology has been of lasting importance, not only in geometrical investigations, but in many other mathematical fields that use topological tools. Spanier-Whitehead duality theory and Alexander-Spanier cohomology are basic theoretical tools; the latter has recently been used to solve problems in dynamical systems theory. In 1966 Spanier published the first comprehensive textbook in algebraic topology: it is still in wide use as a text and standard reference.
After gaining his doctorate at the University of Michigan in 1947, under the direction of Norman Steenrod, Spanier held a postdoctoral fellowship at the Institute for Advanced Study in Princeton, N.J. In 1948 he joined the faculty of mathematics at the University of Chicago. He left Chicago in 1959 to accept appointment as Professor of Mathematics in Berkeley where he taught and continued his research until his retirement in 1991. Shortly after his move west, Spanier undertook the study of formal languages, a subject of importance in computer science. While continuing his research in topology, he published a series of papers about formal languages, many of them jointly with Seymour Ginsburg of the University of Southern California. During his long and distinguished career, Spanier held numerous visiting positions at universities and research institutes throughout the world, including a Guggenheim Fellowship in 1952-53 and a Fulbright Distinguished Lectureship in 1972.
Spanier moved to Scottsdale, Arizona in 1993 and is survived there by his wife, Marianne. In California he leaves three children, Rita Wolenik of Rancho Palos Verdes, Gail Petrek, and Lawrence Spanier, both of Danville, and eight grandchildren. His sister, Leila Rutstein, resides in Silver Spring, Maryland, and his brother, Jerome Spanier, lives in Claremont, California.
A memorial for Edwin Spanier was held November 24, 1996 at the Faculty Club on the UC Berkeley Campus.
Robert Sanders
Hans-Joachim Bremermann was a pioneering biomathematician whose interests ranged widely from artificial intelligence and the limits of computer computation to the purpose of sexual reproduction. He was also professor emeritus of biophysics and mathematics at the University of California at Berkeley.
A native of Bremen, Germany, Bremermann made significant contributions to many areas of mathematics, most importantly in models of biological processes. He was a pioneer in complexity theory and genetic algorithms, and is well known for his models of parasite-host interactions.
He was one of the original creators of genetic algorithms, computer programs that evolve or change in a manner similar to Darwinian evolution. This work led to the concept known as the Bremermann limit, a theoretical limit to any computation.
His theory of sexual reproduction emerged from theoretical musing on why animals would choose to gamble on sexual reproduction when asexual cloning seems a more certain way of assuring survival of offspring. His conclusion was that sexual reproduction arose as response to microscopic parasites, a way of slightly altering the offspring's genetics to throw parasites off track and provide an edge in the constant battle with pathogens.
He also applied discoveries about how bacteria locate food and avoid poisons to create the Bremermann optimizer, a "dumb" but efficient way to perform a search. This concept was later applied to learning by neural networks, artificial circuits designed to mimic networks of brain cells.
In the years before his death, Bremermann worked with immunologists on mathematical models of how HIV interacts with the immune system to cause AIDS.
He also was at work on the theory of dreams, which he proposed as the key to the human brain's ability to recognize patterns. He proposed that the shifting images in our dreams are a window into how the brain analyzes and stores visual patterns. In July 1995, he spoke about his theory of dreams in an invited lecture at the Dalai Lama's 60th birthday celebration in India.
A member of the UC Berkeley Department of Mathematics for more than 30 years, Bremermann gradually diverged from pure mathematics. He joined the Department of Medical Physics in 1970 and eventually ended up in the division of biophysics and cell physiology in the Department of Molecular and Cell Biology. He retired in 1991.
Born September 14, 1926, Bremermann remained in Bremen with his family through World War II. In 1946, he enrolled in the University of Munster where he studied the mathematics of several complex variables and the theory of computation. After obtaining his doctorate in mathematics in 1951, he was able to arrange two years of postdoctoral studies in the United States, at Stanford and Harvard. He was twice invited to conduct research at the Institute for Advanced Study in Princeton, first as a mathematician in 1955 and again as a physicist in 1958.
It was at the Institute, then the "center of the world in mathematics," that Bremermann became involved with programming one of the first computers, MANIAC, constructed by mathematician John von Neumann. During this time he became intrigued by the limits of computing, beginning a life-long interest in developing algorithms or short-cuts for solving complex problems.
In 1959, Bremermann joined the Department of Mathematics at UC Berkeley and quickly took over a seminar in artificial intelligence. In the 1960's he began to collaborate with the Panoramic Research Group in Palo Alto, California, on the first artificial intelligence groups.
In 1995 he received a lifetime achievement award from the Evolutionary Programming Society for his contributions to the foundations of the field and for his work on genetic algorithms. A Fellow of the American Association for the Advancement of Science, Bremermann was a member of the American Mathematical Society as well as a number of other scientific societies in mathematics, artificial intelligence, and biophysics and a founding editor of the Journal of Mathematical Biology.
Bremermann was well known as a warm and patient mentor who nurtured 26 students through their Ph.D. degrees. Many of these students presented Bremermann last year at a banquet in his honor with a Festschrift volume of papers published as a special issue of the journal BioSystems.
Hans-Joachim Bremermann died February 21, 1996 of cancer in Berkeley, California. He is survived by his wife Maribel Bremermann, a native of Spain whom he met while at Stanford in 1954. She is a professor emeritus of romance literature at San Francisco State University.
A memorial service was held on March 17, 1996 in the Faculty Club on the UC Berkeley campus.
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